x(x+1)-8=(x+2)-5x

Solution for x(x+1)-8=(x+2)-5x equation:

x(x+1)-8=(x+2)-5x

We move all terms to the left:

x(x+1)-8-((x+2)-5x)=0

We multiply parentheses

x^2+x-((x+2)-5x)-8=0


We calculate terms in parentheses: -((x+2)-5x), so:

(x+2)-5x

We add all the numbers together, and all the variables

-5x+(x+2)

We get rid of parentheses

-5x+x+2

We add all the numbers together, and all the variables

-4x+2

Back to the equation:

-(-4x+2)


We get rid of parentheses

x^2+x+4x-2-8=0

We add all the numbers together, and all the variables

x^2+5x-10=0

a = 1; b = 5; c = -10;
Δ = b2-4ac
Δ = 52-4·1·(-10)
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{65}}{2*1}=\frac{-5-\sqrt{65}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{65}}{2*1}=\frac{-5+\sqrt{65}}{2}
$